Two identical 9.10-g metal spheres (small enough to be treated as particles) are hung from separate 700-mm strings attached to the same nail in a ceiling. Surplus electrons are added to each sphere, and then the spheres are brought in contact with each other and released. Their equilibrium position is such that each string makes a 17.0° angle with the vertical.
How many surplus electrons are on each sphere?

The number of electrons surplussed on each surface is .

Explanation:

Given:

The masses of the sphere,

The length of the strings,

The angle made by each string with vertical,

According to the diagram, the equilibrium condition for the vertical components of the forces acting on each sphere can be written as

The equilibrium condition for the horizontal components of the forces acting on each sphere can be written as

Here, is the electrostatic force experienced by the metal spheres.

The value of the electrostatic force is given by

Here, is the charge on each sphere and is the distance between them.

Referring to the figure, from ,

Substituting the value of in equation (3), we have

From equation (1),

Substituting the values of and in equation (2), we have

If is the number if electron surplussed with the metal sphere, then

Here, is the electronic charge.

Substituting the value of and in equation (5), we have

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